Sub time-optimal swing up of the acrobot

We consider a variant of the time-optimal control of the acrobot and term it sub time-optimal. By exploiting the partially linearized structure obtained through a feedback linearization technique, we swing up the first link to the vertically upright position in optimal time and then stabilize the second link around its vertical equilibrium position. Rate constraints are imposed on the actuator and certain interesting facts of such an approach are illustrated. Along the way we also prove the “normal” property of the time-optimal control problem for the acrobot.